clients will be configured (in JSCommunicator or whatever client you use) to connect to sip-ws-server.example.org. The server will present a TLS certificate containing the name sip-ws-server.example.org to satisfy the security expectations of the WebSocket client.

the SIP messages will simply contain the name example.org and only example.org is used in the RecordRouteUri parameter. This is important.

WebSockets is a mechanism for creating sockets from a web browser (typically running Javascript) to a server.

draft-ietf-sipcore-sip-websocket defines a way to use WebSockets formally as a transport for SIP. It is not possible to simply view the WebSocket as a tunnel and pass SIP messages through them. Specfically, SIP user agents and proxies must behave slightly differently when WebSockets is used instead of UDP or TCP, and the draft specifies what this means in practice. Code for implementing this protocol was developed on a branch and has subsequently been merged into the trunk for eventual release in reSIProcate 1.9.

WebRTC is related to WebSockets, but it is not the same thing. WebRTC specifies a way for a browser to act as an RTC endpoint, but not specifically as a SIP endpoint. There are SIP implementations written in Javascript that use the WebSocket transport to create WebRTC sessions, and a correctly adapted repro proxy server should be able to interact with such clients.